Understanding the surprising narrowness of eccentric debris belts

Title: Eccentric debris belts reveal the dynamical history of the companion exoplanet

Authors: Laetitia Rodet, and Dong Lai

First author’s institution: Cornell Center for Astrophysics and Planetary Science, Department of Astronomy, Cornell University, Ithaca, NY 14853, USA

Status: Published on ArXiV, 11 August 2022, Submitted to MNRAS

In addition to the eight planets in our solar system, there are two interesting regions containing significantly increased densities of smaller bodies: the asteroid belt located between Mars and Jupiter, and the Kuiper belt at the very edge of the solar system. These belts are made up of what is leftover from the formation period of the solar system, namely planetesimals, objects that are just not massive enough to have become planets themselves.  For this reason, these belts are also known as debris belts.

Figure 1: ALMA image of the HD 53143 debris belt.  Image credit: ALMA / ESO / NAOJ / NRAO / M. MacGregor, University of Colorado, Boulder / S. Dagnello, NRAO, AUI & NSF.

Debris belts aren’t just found around our Sun, but also around other stars. Collisions between planetesimals continuously produce a population of smaller dust grains, which allows for the detection of these extrasolar debris belts. Some of these debris belts are eccentric (the non-circularity of an orbit), such as the debris belt around HD 53143, a star located 60 light years away, depicted in Fig 1. The reason for this eccentricity is a planetary companion on an eccentric orbit forcing the planetesimals in the debris belt into a similar orbit. A surprising observation has been that the width of these eccentric belts is significantly narrower than what one would naively expect. The authors of today’s paper are investigating two possible pathways of achieving such narrow debris disks.

Incoherence of planetesimal orbits determines the width of the debris belt

While individual planetesimals in the debris belt may have similar semi-major axes and eccentricities, the orientation of their orbits in space could be incoherent. This is shown in Fig. 2. The eccentricity of the resulting debris belt is equal to the forcing eccentricity of the exoplanet companion. The width of the belt on the other hand is proportional to what is called the ‘free eccentricity’ — a measure of the degrees of freedom associated with the non-circularity of individual orbits, or in other words, the variation of the orientations of individual orbits.

Figure 2: The incoherence of individual planetesimal orbits (left panels) determines the width of the resulting debris belt (right panel). The quantitative measure of this is called free eccentricity Figure 1 in the paper.

A gas disk can damp eccentricity

The first mechanism discussed by today’s authors that decreases the width of the debris belt, or in other words decreases its free eccentricity, arises when considering the interaction with the planetesimal belt and a still existing protoplanetary disk. Such a system of protoplanetary disk and debris belt distinctly coexisting is known as a transition disk. The idea is that the gas in the protoplanetary disk exerts a drag force on the planetesimals in the debris belt thus damping its free eccentricity, increasing its coherence and thus narrowing its width. However, the authors’ analysis suggests that this effect likely cannot explain all observed eccentric, narrow debris belts due to requiring excessively long protoplanetary disk life times.

Figure 3: An example of a random walk simulation conducted in today’s paper. Shown is the path of the planet in black and the debris belt in blue in the so-called complex eccentricity space. In this space, both orbital eccentricity and the orientation of the orbit are mapped onto a single axis. The width of the debris belt after the simulation finished correlates with the radius of the orange circle. The takeaway is that a significant number of these random walk simulations led to narrow debris belts. Figure 5 in the paper.

Planet-planet scattering

Another way of reducing free eccentricity of the debris belt is to have the forcing planet’s eccentricity increase in time. This can happen if the planet is scattered through interactions with other planets. The authors of today’s paper investigate this process by modeling the planet’s eccentricity growth with a random walk. One example of such a random walk is shown in Fig. 3. The axes in this figure correspond to two orbital elements that correlate to both eccentricity and orbit orientation. The author’s performed many of these random experiments in order to assess to what extent planet-planet scattering and the associated changes in eccentricity can render the planetesimal orbits in the debris belt more coherent. And indeed, they find that a significant fraction of their random simulations do result in a narrow debris belt with coherent planetesimal orbits.

The authors conclude that both protoplanetary disk damping and planet-planet scattering can play an important role in shaping the shape of the debris belt. The inference is that the observation of an narrow eccentric debris disk carries crucial information on the dynamical history of the entire system.

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About Konstantin Gerbig

I'm a PhD student in Astronomy at Yale University. I'm interested in the theory of (Exo)planets and protoplanetary disks and do hydro simulations thereof. I also like music, as well as dancing salsa and tango.

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